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Credit: Vatican Museum
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Introduction
The first rigorous mathematical calculation of $\pi$ was due to Archimedes (ca. 250 BCE), who used a scheme of inscribed and circumscribed polygons to obtain the bounds $3 \frac{10}{71} < \pi < 3 \frac{1}{7}$. The fifth century Indian mathematician Aryabhata produced four digits; the Chinese mathematician Tsu Chung-Chih produced seven. Following the discovery of calculus by Newton and Leibniz in the 1600s, several new formulas for $\pi$ were found.
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